Myanmar is cracking down on Buddhist extremism, aiming to curb ethnic and religious tension that saw two mosques destroyed and scores of Muslim residents fleeing their villages in recent weeks.

Nobel Peace Prize winner and government leader Aung San Suu Kyi has come under criticism from human rights activists and lawyers for not cracking down on the perpetrators of the attacks aimed at the Muslim minority.

In an apparent response to the criticism, the government has made a surprisingly decisive move against an organisation of radical nationalist monks, known as the Ma Ba Tha, threatening legal action if it spread hate speech and incites violence.

Today the government launched a taskforce to prevent violent protests as part of a broader push to stop religious violence.

Religious tension simmered in Buddhist-majority Myanmar for almost half a century of military rule, before boiling over in 2012 in the west of the country into clashes between Rohingya Muslims and ethnic Rakhine Buddhists.

Violence between Muslims and Buddhists in other areas followed in 2013 and 2014.

President Htin Kyaw said in a statement the taskforce will not only move against violent protesters, but also investigate and hold accountable anyone inciting violence.

"We do not want to disturb peaceful protests, but we do not allow violence while protesting," said Zaw Htay, spokesman of the state councillor's office occupied by Suu Kyi.

A government-appointed body that oversees Myanmar's Buddhist monkhood, the State Sangha Maha Nayaka Committee, issued a statement this week, saying it had never endorsed the nationalist and anti-Muslim Ma Ba Tha.

In June, a group of 200 villagers destroyed a mosque and injured a Muslim man in central Myanmar after a dispute over the construction of a Muslim school.

In a separate incident in northern Myanmar in early July, nearly 500 Buddhists burned down a Muslim prayer hall. Police arrested five in connection with the attack, media said.

In both incidents, Muslim residents fled from their homes fearing more widespread violence.

Some 125,000 Rohingya Muslims displaced by the 2012 violence remain in camps in the west.